A number of custody arrangements are possible. The most common are:

Joint Legal Custody: This means that both parents have the right to participate in the important decisions regarding the child(ren)’s upbringing.  All major decisions regarding medical care, education and religion shall be shared by both parents. 

Sole Custody: This means that only one has the exclusive right to make the important decisions regarding the child(ren)’s upbringing, medical care, education and religion. 

Joint Physical Placement: This means that children reside with one parent part of the time and the other parent part of the time. The parent who has care of the children at any given time is responsible for routine decisions.

Primary Physical Placement: This means that the child(ren) primarily resides with one parent.

Parents are encouraged to reach their own agreements regarding custody. When parents cannot agree, the Court must decide by considering all of the following factors of the Michigan Child Custody Act. MCL 722.23

(a) The love, affection and other emotional ties existing between the parties involved and the child.
(b) The capacity and disposition of the parties involved to give the child love, affection and guidance and the continuation of the educating and raising of the child in its religion or creed, if any.
(c) The capacity and disposition of the parties involved to provide the child with food, clothing, medical care and other remedial care recognized and permitted under the laws of this state in place of medical care, and other material needs.
(d) The length of time the child has lived in a stable, satisfactory environment, and the desirability of maintaining continuity.
(e) The permanence, as a family unit, of the existing or proposed custodial home or homes.
(f) The moral fitness of the parties involved.
(g) The mental and physical health of the parties involved.
(h) The home, school and community record of the child.
(i) The reasonable preference of the child, if the court considers the child to be of sufficient age to express preference.
(j) The willingness and ability of each of the parents to facilitate and encourage a close and continuing parent-child relationship between the child and the other parent.
(k) Domestic violence, regardless of whether the violence was directed against, or witnessed by the child. 
(l) Any other factor considered by the court to be of relevance to a particular child custody dispute.

Michigan Custody Guideline Handbook

Access to child(ren)'s records for non-custodial parents