The canons have been revisited here several times. I live in an area in which there are multiple cross juristdictional territories, Maronite, Ruthenian, Ukrainian, and Roman. According to the same canons which have been already quoted, all that is necessery is that the hierarch of origin agrees to release the individual to a requesting hierarch after a petition is made. The Apostolic See’s approval is presumed in a case such as this. Note, there is no statement in any of the canons in this circumstance that the applicant is required to sign another document. This very canon actually states the acceptance to be very simple.
The receiving ritual church may have it’s own requirements for documentaion of a personal declaration with witnesses, such as occurs in the Byzantine Catholic Church USA. Very Rev. Robert J. Hospidar, J.C.L. requires that a form be signed by the person and two witnesses, and then returned, and that the transfer is not achieved until the Chancellor notarized protocol is received by the faithful transfering.
Of course, per the Latin rescript in 1992, it is acceptable to the Holy See if the two bishops agree in writing.
AAS 85 [1983] 81:
Acta Ioannis Pauli Pp. II
SECRETARIA STATUS
Fit facultas licentiam de qua in can. 112, 1, 1 C.I.C. legitime, in casu, praesumenda.
RESCRIPTUM EX AUDIENTIA SS.MI
Ad normam can. 112, 1, I Codicis Iuris Canonici, quisque vetatur post susceptum Baptismum alii ascribi Ecclesiae rituali sui iuris, nisi licentia ei facta ab Apostolica Sede. Hac de re, probato iudicio Pontificii Consilii de Legum Textibus Interpetandis, Summus Pontifex Ioannes Paulus II statuit eiusmodi licentiam praesumi posse, quoties transitum ad aliam Ecclesiam ritualem sui iuris sibi petierit Christifidelis Ecclesia Latinae, quae Eparchiam suam intra eosdem fines habet, dummodo Episcopi diocesani utriusque dioecesis in id secum ipsi scripto consentiant.
Ex Audientia Sanctissimi, die xxvi mensis Novembris, anno MCMXCII.
ANGELUS card. SODANO
Secratarius Status