What is the test for retaining a retained or appointed attorney in a civil matter?

[440 P.2d 75] We conclude that the constitutional guarantee of the defendant's right to counsel requires that his advocate, whether retained or appointed, be free in all cases of the threat that he may be summarily relieved as 'incompetent' by the very trial judge he is duty-bound to attempt to convince of the rightness of his client's cause. Here, as in Gallagher v. Municipal Court (1948) supra, 31 Cal.2d 784, 797, 192 P.2d 905, 914, 'the recognition of such an authority would involve the surrender of a substantial amount of the independence of the bar, and in many instances would deprive litigants of a fair hearing.'