Most deacons, just like most priests, are assigned by their bishops to a parish ministry. However, there are some things that should be realized, especially by anyone interested in a vocation as a deacon.
Second, this means that one of the first things new applicants to the diaconate have to realize is that they will NOT be ordained for service in the parish from which they are applying, and that there is no guarantee that they will be assigned to that parish should they be called to ordination. This is something the applicant and his family need to consider carefully! If they've been lifelong members of the same parish, they may be unwilling to change that reality. Of course, what many families decide to do is keep their parish membership at the original parish, while the deacon accepts his diaconal assignment to another parish. Now, in reality, no bishop is going to assign a deacon to a ministry that would require his family to uproot themselves to a different part of the diocese. But he may very well determine that a particular deacon's talents are needed more in a parish across town, or in a ministry outside his original parish.
Third, it needs to be remembered that, increasingly, deacons are given assignments in SEVERAL areas. Many deacons now serve in more than one parish, or in at least one parish in addition to assignments to regional or diocesan ministries. For example, I currently have an assignment to a local parish, but also an assignment to serve in campus ministry at the University in which I teach. In fact, many dioceses now expect their deacons to have at least TWO assignments: one to a parish (at least one) and another to a diocesan or deanery-based ministry (e.g., jail/prison ministry, hospitals, and so on).
Applicants to the diaconate and those in formation must expand their sense of church and the role of deacons within that church. Ordination in the Catholic Church is NEVER to a parish alone, but to the diocese as the bishop directs. This often requires quite a shift in thinking.
In 1996, the bishops of the US published the results of a year-long study of the diaconate in the United States. The study included responses from lay leaders, priests, deacons and the wives of deacons. One of the many interesting things that was revealed was this: Many people, when asked about the ministry of PRIESTS, described them as diocesan ministers currently assigned to a parish. When asked the same question about DEACONS, they were almost always described as parish ministers only. The bishops listed this misperception as something that needed to be corrected as quickly as possible.
Why is this such a big deal? Well, first, because of the challenge this presents to those in formation; they need to understand what they're getting into! Second, because the reasons the diaconate was renewed in the Catholic church was to extend the reach of the bishop's ministry into areas not currently being met. In other words, parish priests are focused on parishes; that's what we expect of them. Deacons, on the other hand, are supposed to extend BEYOND the parish; that's what we should be expecting of them.
One final note: Deacons as parish ministers has been the experience of many churches and denominations other than the Catholic church. Protestant deacons, for example, are often more like congregational trustees, although in many "high churches" (such as in the Anglican communion) and increasingly in many Methodist and Lutheran churches, deacons are understood as ordained for more than parish ministries.